In recent years, total variation (TV) regularization has become a popular and powerful tool for image restoration and enhancement. In this work, we apply TV minimization to improve the quality of dynamic magnetic resonance images. Dynamic magnetic resonance imaging is an increasingly popular clinical technique used to monitor spatio-temporal changes in tissue structure. Fast data acquisition is necessary in order to capture the dynamic process. Most commonly, the requirement of high temporal resolution is fulfilled by sacrificing spatial resolution. Therefore, the numerical methods have to address the issue of images reconstruction from limited Fourier data. One of the most successful techniques for dynamic imaging applications is the reduced-encoded imaging by generalized-series reconstruction method of Liang and Lauterbur. However, even if this method utilizes a priori data for optimal image reconstruction, the produced dynamic images are degraded by truncation artifacts, most notably Gibbs ringing, due to the spatial low resolution of the data. We use a TV regularization strategy in order to reduce these truncation artifacts in the dynamic images. The resulting TV minimization problem is solved by the fixed point iteration method of Vogel and Oman. The results of test problems with simulated and real data are presented to illustrate the effectiveness of the proposed approach in reducing the truncation artifacts of the reconstructed images.